You need to add an UV protectant after doing this, or your lenses will haze up again even faster and within 1 year, since the factory UV protection has now been removed. Carwax may only be a partial solution, and is a pain to do so frequently. This is the dirty secret of headlight polishing.
I do think the permanant way to resolve this is to get Paint protection film (3m/xpel/etc). This may cost you up to $100 from a clearbra installer.